Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
# include <iostream>
# include <algorithm>
# include <vector>
# include <string>
# include <set>
# include <map>
# include <cmath>
# include <iomanip>
# include <functional>
# include <utility>
# include <stack>
# include <queue>
# include <list>
# include <tuple>
# include <unordered_map>
# include <numeric>
# include <complex>
# include <bitset>
# include <random>
# include <chrono>
# include <cstdlib>
# include <tuple>
# include <array>
using namespace std;
using LL = long long;
using ULL = unsigned long long;
using D = double;
constexpr int INF = 2147483647;
constexpr int HINF = INF / 2;
constexpr double DINF = 100000000000000000.0;
constexpr double HDINF = 50000000000000000.0;
constexpr long long LINF = 9223372036854775807;
constexpr long long HLINF = 4500000000000000000;
const double PI = acos(-1);
template <typename T_char>T_char TL(T_char cX) { return tolower(cX); };
template <typename T_char>T_char TU(T_char cX) { return toupper(cX); };
typedef pair<LL, LL> pii;
const int vy[] = { -1, -1, -1, 0, 1, 1, 1, 0 }, vx[] = { -1, 0, 1, 1, 1, 0, -1, -1 };
const int dx[4] = { 0,1,0,-1 }, dy[4] = { 1,0,-1,0 };
int popcnt(unsigned long long n) { int cnt = 0; for (int i = 0; i < 64; i++)if ((n >> i) & 1)cnt++; return cnt; }
int d_sum(LL n) { int ret = 0; while (n > 0) { ret += n % 10; n /= 10; }return ret; }
int d_num(LL n) { int ret = 0; while (n > 0) { ret++; n /= 10; }return ret; }
LL gcd(LL a, LL b) { if (b == 0)return a; return gcd(b, a%b); };
LL lcm(LL a, LL b) { LL g = gcd(a, b); return a / g*b; };
# define ALL(qpqpq)           (qpqpq).begin(),(qpqpq).end()
# define RALL(qpqpq)           (qpqpq).rbegin(),(qpqpq).rend()
# define UNIQUE(wpwpw)        sort(ALL((wpwpw)));(wpwpw).erase(unique(ALL((wpwpw))),(wpwpw).end())
# define LOWER(epepe)         transform(ALL((epepe)),(epepe).begin(),TL<char>)
# define UPPER(rprpr)         transform(ALL((rprpr)),(rprpr).begin(),TU<char>)
# define FOR(i,tptpt,ypypy)   for(LL i=(tptpt);i<(ypypy);i++)
# define RFOR(i,tptpt,ypypy)  for(LL i=(tptpt);i>=(ypypy);i--)
# define REP(i,upupu)         FOR(i,0,upupu)
# define INIT                 std::ios::sync_with_stdio(false);std::cin.tie(0)

int n;
double a[1010];
vector < pair<double, int>>v;
int main() {
	cin >> n;
	REP(i, n) {
		cin >> a[i];
		v.emplace_back(make_pair(a[i], i));
	}
	double ans = -INF;
	sort(ALL(v));
	reverse(ALL(v));
	REP(i, n) {
		REP(j, n) {
			if (i == j)continue;
			double num[2];
			int cur = 0;
			REP(k, n) {
				if (cur == 2)break;
				if (v[k].second == i || v[k].second == j)continue;
				num[cur] = v[k].first;
				cur++;
			}
			ans = max(ans, (num[0] + num[1]) / abs(a[i] - a[j]));
		}
	}
	cout<<fixed<<setprecision(13) << ans << endl;
}